Paper
Sharp decay for Teukolsky equation in Kerr spacetimes
Authors
Siyuan Ma, Lin Zhang
Abstract
In this work, we derive the global sharp decay, as both a lower and an upper bounds, for the spin components, which are solutions to the Teukolsky equation, in the black hole exterior and on the event horizon of a slowly rotating Kerr spacetime. These estimates are generalized to any subextreme Kerr background under an integrated local energy decay estimate. Our results apply to the scalar field , the Maxwell field and the linearized gravity and confirm the Price's law decay that is conjectured to be sharp. Our analyses rely on a novel global conservation law for the Teukolsky equation, and this new approach can be applied to derive the precise asymptotics for solutions to semilinear wave equations.